Spectral resolution for a five-element, filtered, x-ray detector array using the method of Backus and Gilbert

The generalized method of Backus and Gilbert (BG) is described and applied to the inverse problem of obtaining the spectrum from a five-channel, filte red array of x-ray detectors. This diagnostic is routinely fielded on the Z facility at Sandia National Laboratories to study soft x-ray photons (simi lar to 100-2300 eV), emitted by high density Z-pinch plasmas. The BG method defines spectral resolution limits on the system of response functions tha t are in good agreement with a classical unfold method, based on a histogra m representation of the source spectrum. The resolution so defined is indep endent of the source spectrum. For noise-free, simulated data the BG approx imating function is also in reasonable agreement with the source spectrum ( 150 eV blackbody) and the unfolded spectrum. This function may be used as a n initial trial function for iterative methods or a regularization model. ( C) 2000 American Institute of Physics. [S0034-6748(00)01508-2].